Throughout his presidency a doubt about Barack Obama has lingered, one that first surfaced during his campaign for the White House that began nearly four years ago. The fear was that – for all his oratorical brilliance – Obama somehow lacked empathy, that he was a slightly chilly, aloof figure, that he struggled to connect emotionally.

We'll hear much less of that talk now.

For the address he gave at last night's memorial service for the victims of the Arizona shootings was elegiac, heartfelt and deeply moving. It both rose to the moment and transcended it: after days of noise and rancour, he carved out a moment of calm.

Much of the speech was dedicated to its core function: to commemorate the dead and comfort those in mourning. He spoke in detail about those who had been slain, describing them one by one – the elderly couple who had lived life as if it were a "50-year honeymoon", the husband who shielded his wife from the bullets, dying so that she might live. Most affecting, he spoke of Christina Taylor Green, the nine-year-old girl born on 11 September 2001 – the president, doubtless thinking of his own daughters, seeming to brim with emotion, at one point emitting a noise somewhere between a sigh and a suppressed sob.

In all this, he spoke less like a politician than a pastor or priest comforting a grieving community. The focus on those who had saved lives was an attempt to offer hope amid the sadness: "Heroism is here," he said, an echo of his own famous declaration that "We are the ones we have been waiting for." He reminded his flock of what really mattered: it was "not wealth, or status, or power, or fame – but rather, how well we have loved".

This is part of the US presidential job description that sets the office apart: more than mere head of government, an American president is required to be almost a spiritual leader to his nation. Obama ascended to that role in Tucson yesterday, with no less aplomb than Bill Clinton summoned in Oklahoma City in 1995.

For all that, such a moment will – inevitably – have political reverberations. This was no ordinary memorial service – that much was clear from the cheers and ovations that greeted frequent chunks of the stadium speech (and that might have grated on some ears). What, besides proving Obama's ability to empathise, will be the political impact?

Crude though it is to say so, it will have boosted the president's standing enormously. After the partisan bickering that followed Saturday's killings, Obama stepped forward to be what analyst Nate Silver called "the adult in the room". This was meant to be the Republicans' week, as they took control of the House of Representatives and its legislative agenda. Instead they look small – as well as defensive, fending off accusations that it was the violent rhetoric of the right that fuelled the current toxic political environment. None smaller than the de facto leader of today's Republican party, Sarah Palin, who preceded the Tucson address with an aggressive, self-regarding and petty-minded videotaped message that claimed she had been the victim of a "blood libel". The contrast between the two performances could not have been sharper.

Obama looks the bigger person, calling for a discourse that heals not wounds. That puts him in the place all presidents covet: above the fray, beyond mere Democrat or Republican. Ronald Reagan got there, but few others manage it. The challenge will be to maintain that position into the re-election year of 2012.

But such thoughts are for later. What will be remembered today are moments like those when he told his audience that Gabrielle Giffords had opened her eyes for the first time – moments when only the most cold-hearted would not have felt a tear. What we saw from Obama in Tucson will be a defining, even cherished moment in his presidency.

Hundreds line Tucson's streets to pay respects to Christina Taylor Green, nine, the youngest victim of the gun attack by Jared Lee Loughner that left six dead and congresswoman Gabrielle Giffords fighting for her life